Several studies have been made to understand the behavior of Total Electron Content (TEC) in the topside of the ionosphere during two types of geomagnetic storms. The aim of this research is to examine the ionospheric disturbances using the TEC parameter during the great and severe geomagnetic storms that occurred during the period (28-30 October 2003). Theexamination was conducted for the region,includingIraq and surrounding areas that cover the arealatitude 27-39^oN; longitude 27-54^oE). TEC data were obtained fromthe Defense Meteorological Satellite Program (DMSP), to determine the type of geomagnetic storm, the Disturbance storm time (Dst) index was gathered for the selected days from the website Koyota, Japan WDC.Fromthe results,it wasfound that there was a good relationship between Dst-indexand TEC parameter values. There is a discrepancy in observations recorded about TEC values during the period of geomagnetic storms.There were significant enhancements in the values of TEC during storms; however, there was an anomaly when the storm continued for several hours during the day, there was a highly broad increase in TEC from sunrise to sunset. Moreover, when two types of storms occurred, two peaks or more appeared, and they remained for one event, or even for more than one day. Comparisons between the observed TEC and the predicted values were applied in order to check the validity of the IRI-20 ionospheric model during the storm time above the mid-latitude studiedareas;it found that there is a non-linear correlation between them withi24 hours and three days, so the model wouldneed some modification in the future to be suitable for the Iraq region during storm time.